Abstract
A k-track drawing is a crossing-free 3D straight-line grid drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing is called the track number of G. In the existing literature a lower bound of five and an upper bound of fifteen are known for the track number of series-parallel graph. In this paper we reduce this gap for a large subclass of series-parallel graph for which the lower bound remains five but we show an upper bound of eight. We also describe a linear time drawing algorithm that computes a 3D straight-line grid drawing of these graphs in volume 4 × 4 × 2n.
Research supported in part by “Progetto ALINWEB: Algoritmica per Internet e per il Web”, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale.
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Di Giacomo, E. (2004). Drawing Series-Parallel Graphs on Restricted Integer 3D Grids. In: Liotta, G. (eds) Graph Drawing. GD 2003. Lecture Notes in Computer Science, vol 2912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24595-7_22
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DOI: https://doi.org/10.1007/978-3-540-24595-7_22
Publisher Name: Springer, Berlin, Heidelberg
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